Preservation of Perfectness and Acyclicity: Berrick and Casacuberta's Universal Acyclic Space Localized at a Set of Primes

Abstract In this paper we answer negatively a question posed by Casacuberta, Farjoun, and Libman about the preservation of perfect groups under localization functors. Indeed, we show that a certain P-localization of Berrick and Casacuberta's universal acyclic group is not perfect. We also investigate under which conditions perfectness is preserved: For instance, we show that if the localization of a perfect group is finite then it is perfect.